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https://github.com/coq-community/stalmarck
Certified implementation in Coq of Stålmarck's algorithm for proving tautologies [maintainer=@palmskog]
https://github.com/coq-community/stalmarck
coq coq-ci coq-extraction coq-plugin docker-coq-action nix-action tautology tautology-checking
Last synced: about 2 months ago
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Certified implementation in Coq of Stålmarck's algorithm for proving tautologies [maintainer=@palmskog]
- Host: GitHub
- URL: https://github.com/coq-community/stalmarck
- Owner: coq-community
- License: lgpl-2.1
- Created: 2016-04-27T17:17:03.000Z (over 8 years ago)
- Default Branch: master
- Last Pushed: 2024-06-30T08:07:58.000Z (7 months ago)
- Last Synced: 2024-07-01T17:50:39.470Z (7 months ago)
- Topics: coq, coq-ci, coq-extraction, coq-plugin, docker-coq-action, nix-action, tautology, tautology-checking
- Language: Coq
- Homepage:
- Size: 375 KB
- Stars: 1
- Watchers: 6
- Forks: 3
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# Stalmarck
[![Docker CI][docker-action-shield]][docker-action-link]
[![Nix CI][nix-action-shield]][nix-action-link]
[![Contributing][contributing-shield]][contributing-link]
[![Code of Conduct][conduct-shield]][conduct-link]
[![Zulip][zulip-shield]][zulip-link]
[![DOI][doi-shield]][doi-link]
[docker-action-shield]: https://github.com/coq-community/stalmarck/actions/workflows/docker-action.yml/badge.svg?branch=master
[docker-action-link]: https://github.com/coq-community/stalmarck/actions/workflows/docker-action.yml
[nix-action-shield]: https://github.com/coq-community/stalmarck/actions/workflows/nix-action.yml/badge.svg?branch=master
[nix-action-link]: https://github.com/coq-community/stalmarck/actions/workflows/nix-action.yml
[contributing-shield]: https://img.shields.io/badge/contributions-welcome-%23f7931e.svg
[contributing-link]: https://github.com/coq-community/manifesto/blob/master/CONTRIBUTING.md
[conduct-shield]: https://img.shields.io/badge/%E2%9D%A4-code%20of%20conduct-%23f15a24.svg
[conduct-link]: https://github.com/coq-community/manifesto/blob/master/CODE_OF_CONDUCT.md
[zulip-shield]: https://img.shields.io/badge/chat-on%20zulip-%23c1272d.svg
[zulip-link]: https://coq.zulipchat.com/#narrow/stream/237663-coq-community-devs.20.26.20users
[doi-shield]: https://zenodo.org/badge/DOI/10.1007/3-540-44659-1_24.svg
[doi-link]: https://doi.org/10.1007/3-540-44659-1_24
A two-level approach to prove tautologies using Stålmarck's
algorithm in Coq.
## Meta
- Author(s):
- Pierre Letouzey (initial)
- Laurent Théry (initial)
- Coq-community maintainer(s):
- Karl Palmskog ([**@palmskog**](https://github.com/palmskog))
- License: [GNU Lesser General Public License v2.1 or later](LICENSE)
- Compatible Coq versions: Coq master (use the corresponding branch or release for other Coq versions)
- Additional dependencies: none
- Coq namespace: `Stalmarck.Algorithm`
- Related publication(s):
- [Formalizing Stålmarck's Algorithm in Coq](https://www.irif.fr/~letouzey/download/stalmarck.ps.gz) doi:[10.1007/3-540-44659-1_24](https://doi.org/10.1007/3-540-44659-1_24)
## Building and installation instructions
The easiest way to install the latest released version of Stalmarck
is via [OPAM](https://opam.ocaml.org/doc/Install.html):
```shell
opam repo add coq-released https://coq.inria.fr/opam/released
opam install coq-stalmarck
```
To instead build and install manually, do:
``` shell
git clone https://github.com/coq-community/stalmarck.git
cd stalmarck
make # or make -j
make install
```
## Documentation
This project is composed of:
- A Coq proof of correctness of the algorithm, as described in the paper
[A Formalization of Stålmarck's Algorithm in Coq][paper-link], published
in the proceedings of TPHOLs 2000.
- an implementation of the algorithm. With respect to the paper, this
implementation is completely functional and can be used inside Coq.
- A reflected Coq tactic `staltac` that uses the extracted code to compute
an execution trace; the trace checker is then called inside Coq.
- A standalone checker program `stalmarck` which takes as input a formula in
textual format and reports whether it can be certified as a tautology.
See `algoRun.v` for examples how to use the algorithm inside Coq, and
see `StalTac_ex.v` for examples how to use the reflected tactic.
[paper-link]: https://www.irif.fr/~letouzey/download/stalmarck.ps.gz
## Tautology Checker
The `src` directory contains the code for a standalone tautology checker
using the implementation of Stålmarck's algorithm extracted from Coq.
### Running the checker
```shell
stalmarck
```
where:
- `` is an integer controling depth of dilemma. Usual values:
- 0: does only propagation.
- 1: dilemma upon one variable at the same time.
- 2: dilemma can be done upon two variables at the same time; more than 2 may take *very* long.
- `` is the file containing the boolean formula.
## Boolean formula syntax
| Concept | Syntax |
| -------- | ------ |
| Comments | `//` (reading is suspended until the end of the line) |
| Variable | any alphanumeric sequence plus the character `_` |
| Not | `~` |
| And | `&` |
| Or | `#` |
| Implication | `->` |
| Equivalence | `<->` |
| Parentheses | `( )` |
| True value | `` |
| False value | `` |
Priority of connectives, from lower to higher:
- `<->`, `->` (associate to the right)
- `#` (associates to the left)
- `&` (associates to the left)
- `~`
## Output
The only interesting output is `Tautology` (and exit code 0).
The other output is `Don't know` (and exit code 1): either the formula
is not a tautology, or it is one but the program cannot conclude this
(insufficient level).
## Example
An example file with a tautology ([`tests/ztwaalf1_be`](tests/ztwaalf1_be))
is included, and can be checked as follows:
```shell
stalmarck 1 tests/ztwaalf1_be
Tautology
```